Question

A cuboid have total surface area of 40m2 and its lateral surface area is 26m2 find the area of its base

Answer 1

Hy!!

_______________________

Since Total surface area of a cuboid =
2(lb + bh + lh)

=) 2lb + 2bh + 2lh = 40 m^2 .. Eq. 1.

Since Lateral surface area of a cuboid =
2(l+b) * h

=) 2lh + 2bh = 26 m^2 .. Eq. 2.

Subtract eq 1 from eq 2..

=) 2lb + 2bh + 2lh - (2bh + 2lh) =
40m^2 - 26m^2

=) 2lb + 2bh - 2bh + 2lh - 2lh = 14 m^2

=) 2lb = 14 m^2

=) lb = 14/2 m^2

=) lb = 7 m^2

Since area of a cuboid is lb.

Hence Area of base of a cuboid = 7 m^2.

________________

Hope it's helpful to u.. :)

Answer 2

Answer:

$\small\red{\boxed{\bold{Area \:of \:base\:=7m^2}}}$

$\tt{Given}\begin{cases}\tt{40 \:square \:meter } \\ \tt{lateral\: surface\: area =26}\end{cases}$

$\huge\underline\textsf{Explantion:- }$

$\small\underline\textsf{formula \:used }$

$\implies\bf t.s.a = 2(lb + bh + lh)$

$\implies\bf l.s.a = 2(l + b)h$

$\rule{300}{2}$

$\implies\bf l.s.a = 2(bh + 2lb)$

$\implies\bf40 = 26 + 2lb$

$\implies\bf40 - 26 = 2lb$

$\implies\bf14 = 2lb$

$\implies\bf \frac{\cancel{14}}{ \cancel2} = lb$

$\implies\bf7m {}^{2}$